Solve for $x$ : $x^2 + x - 42 = 0$
Answer: The coefficient on the $x$ term is $1$ and the constant term is $-42$ , so we need to find two numbers that add up to $1$ and multiply to $-42$ The two numbers $-6$ and $7$ satisfy both conditions: $ {-6} + {7} = {1} $ $ {-6} \times {7} = {-42} $ $(x {-6}) (x + {7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -6) (x + 7) = 0$ $x - 6 = 0$ or $x + 7 = 0$ Thus, $x = 6$ and $x = -7$ are the solutions.